Essays on quantile regression for dynamic panel data models

This thesis studies quantile regression methods for dynamic panel data models. Quantile regression for panel data is extremely important in econometrics since it allows the investigator to explore a range of conditional quantile functions thereby exposing a variety of forms of conditional heterogeneity as well as controlling for unobserved individual characteristics.;The first chapter presents an introduction and overview of the manuscript. In the second chapter, we study estimation and inference in a quantile regression dynamic panel model with fixed effects. Panel data fixed effects estimators are typically biased in the presence of lagged dependent variables as regressors; to reduce the dynamic bias in the quantile regression fixed effects estimator we suggest the use of the instrumental variables quantile regression method of Chernozhukov and Hansen (2006, 2008) along with lagged regressors as instruments. We show that the instrumental variables estimator is consistent and asymptotically normal when Na/T → 0, for some a > 0. We briefly describe how to employ the estimated models for prediction. In addition, Wald and Kolmogorov-Smirnov type tests for general linear restrictions are proposed. Monte Carlo is used to evaluate the finite sample properties of the estimators and tests. The simulation results show that the instrumental variables approach sharply reduces the dynamic bias, and turns out to be especially advantageous when innovations are non-Gaussian and heavy-tailed. Finally, we illustrate the procedures by testing for the presence of time non-separability in utility using panel data on household consumption. The results show evidence of asymmetric persistence in consumption dynamics, and important heterogeneity in the determinants of consumption.;The third chapter develops penalized quantile regression methods for dynamic panel data with fixed effects. We consider a penalized strategy designed to improve the properties of the dynamic panel data quantile regression instrumental variables estimator. The penalty involves l1 shrinkage of the fixed effects. We discuss a tuning parameter selector based on the Schwartz information criterion, and propose a bootstrap resampling procedure for constructing confidence intervals for the parameters of interest. Monte Carlo simulations illustrate the dramatic improvement in the performance of the proposed estimator compared with the fixed effects quantile regression instrumental variables estimator. Finally, we provide an application to the partial adjustment toward target capital structures. The results show evidence that there is substantial heterogeneity in the speed of adjustment among firms.